{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Odds and Addends"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "Think Bayes, Second Edition\n",
    "\n",
    "Copyright 2020 Allen B. Downey\n",
    "\n",
    "License: [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](https://creativecommons.org/licenses/by-nc-sa/4.0/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.054803Z",
     "iopub.status.busy": "2021-04-16T19:35:25.054381Z",
     "iopub.status.idle": "2021-04-16T19:35:25.056675Z",
     "shell.execute_reply": "2021-04-16T19:35:25.056251Z"
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# If we're running on Colab, install empiricaldist\n",
    "# https://pypi.org/project/empiricaldist/\n",
    "\n",
    "import sys\n",
    "IN_COLAB = 'google.colab' in sys.modules\n",
    "\n",
    "if IN_COLAB:\n",
    "    !pip install empiricaldist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.060363Z",
     "iopub.status.busy": "2021-04-16T19:35:25.059859Z",
     "iopub.status.idle": "2021-04-16T19:35:25.061547Z",
     "shell.execute_reply": "2021-04-16T19:35:25.061891Z"
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# Get utils.py\n",
    "\n",
    "from os.path import basename, exists\n",
    "\n",
    "def download(url):\n",
    "    filename = basename(url)\n",
    "    if not exists(filename):\n",
    "        from urllib.request import urlretrieve\n",
    "        local, _ = urlretrieve(url, filename)\n",
    "        print('Downloaded ' + local)\n",
    "    \n",
    "download('https://github.com/AllenDowney/ThinkBayes2/raw/master/soln/utils.py')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.064750Z",
     "iopub.status.busy": "2021-04-16T19:35:25.064307Z",
     "iopub.status.idle": "2021-04-16T19:35:25.842409Z",
     "shell.execute_reply": "2021-04-16T19:35:25.841954Z"
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "from utils import set_pyplot_params\n",
    "set_pyplot_params()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This chapter presents a new way to represent a degree of certainty, **odds**, and a new form of Bayes's Theorem, called **Bayes's Rule**.\n",
    "Bayes's Rule is convenient if you want to do a Bayesian update on paper or in your head.\n",
    "It also sheds light on the important idea of **evidence** and how we can quantify the strength of evidence.\n",
    "\n",
    "The second part of the chapter is about \"addends\", that is, quantities being added, and how we can compute their distributions.\n",
    "We'll define functions that compute the distribution of sums, differences, products, and other operations.\n",
    "Then we'll use those distributions as part of a Bayesian update."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Odds\n",
    "\n",
    "One way to represent a probability is with a number between 0 and 1, but that's not the only way.\n",
    "If you have ever bet on a football game or a horse race, you have probably encountered another representation of probability, called **odds**.\n",
    "\n",
    "You might have heard expressions like \"the odds are three to one\", but you might not know what that means.\n",
    "The **odds in favor** of an event are the ratio of the probability\n",
    "it will occur to the probability that it will not.\n",
    "\n",
    "The following function does this calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.847175Z",
     "iopub.status.busy": "2021-04-16T19:35:25.846506Z",
     "iopub.status.idle": "2021-04-16T19:35:25.850491Z",
     "shell.execute_reply": "2021-04-16T19:35:25.850052Z"
    }
   },
   "outputs": [],
   "source": [
    "def odds(p):\n",
    "    return p / (1-p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, if my team has a 75% chance of winning, the odds in their favor are three to one, because the chance of winning is three times the chance of losing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.857515Z",
     "iopub.status.busy": "2021-04-16T19:35:25.856721Z",
     "iopub.status.idle": "2021-04-16T19:35:25.859929Z",
     "shell.execute_reply": "2021-04-16T19:35:25.860503Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds(0.75)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can write odds in decimal form, but it is also common to\n",
    "write them as a ratio of integers.\n",
    "So \"three to one\" is sometimes written $3:1$.\n",
    "\n",
    "When probabilities are low, it is more common to report the\n",
    "**odds against** rather than the odds in favor.\n",
    "For example, if my horse has a 10% chance of winning, the odds in favor are $1:9$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.864570Z",
     "iopub.status.busy": "2021-04-16T19:35:25.863924Z",
     "iopub.status.idle": "2021-04-16T19:35:25.867151Z",
     "shell.execute_reply": "2021-04-16T19:35:25.866535Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11111111111111112"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But in that case it would be more common I to say that the odds against are $9:1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.871386Z",
     "iopub.status.busy": "2021-04-16T19:35:25.870629Z",
     "iopub.status.idle": "2021-04-16T19:35:25.874421Z",
     "shell.execute_reply": "2021-04-16T19:35:25.873817Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.000000000000002"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds(0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the odds in favor, in decimal form, you can convert to probability like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.878254Z",
     "iopub.status.busy": "2021-04-16T19:35:25.877499Z",
     "iopub.status.idle": "2021-04-16T19:35:25.879194Z",
     "shell.execute_reply": "2021-04-16T19:35:25.879785Z"
    }
   },
   "outputs": [],
   "source": [
    "def prob(o):\n",
    "    return o / (o+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, if the odds are $3/2$, the corresponding probability is $3/5$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.884222Z",
     "iopub.status.busy": "2021-04-16T19:35:25.883524Z",
     "iopub.status.idle": "2021-04-16T19:35:25.886020Z",
     "shell.execute_reply": "2021-04-16T19:35:25.886547Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob(3/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or if you represent odds with a numerator and denominator, you can convert to probability like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.890280Z",
     "iopub.status.busy": "2021-04-16T19:35:25.889753Z",
     "iopub.status.idle": "2021-04-16T19:35:25.891691Z",
     "shell.execute_reply": "2021-04-16T19:35:25.892110Z"
    }
   },
   "outputs": [],
   "source": [
    "def prob2(yes, no):\n",
    "    return yes / (yes + no)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.896932Z",
     "iopub.status.busy": "2021-04-16T19:35:25.896240Z",
     "iopub.status.idle": "2021-04-16T19:35:25.899626Z",
     "shell.execute_reply": "2021-04-16T19:35:25.899181Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob2(3, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probabilities and odds are different representations of the\n",
    "same information; given either one, you can compute the other.\n",
    "But some computations are easier when we work with odds, as we'll see in the next section, and some computations are even easier with log odds, which we'll see later."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayes's Rule\n",
    "\n",
    "So far we have worked with Bayes's theorem in the \"probability form\": \n",
    "\n",
    "$$P(H|D) = \\frac{P(H)~P(D|H)}{P(D)}$$\n",
    "\n",
    "Writing $\\mathrm{odds}(A)$ for odds in favor of $A$, we can express Bayes's Theorem in \"odds form\":\n",
    "\n",
    "$$\\mathrm{odds}(A|D) = \\mathrm{odds}(A)~\\frac{P(D|A)}{P(D|B)}$$\n",
    "\n",
    "This is Bayes's Rule, which says that the posterior odds are the prior odds times the likelihood ratio.\n",
    "Bayes's Rule is convenient for computing a Bayesian update on paper or in your head. For example, let's go back to the cookie problem:\n",
    "\n",
    "> Suppose there are two bowls of cookies. Bowl 1 contains 30 vanilla cookies and 10 chocolate cookies. Bowl 2 contains 20 of each. Now suppose you choose one of the bowls at random and, without looking, select a cookie at random. The cookie is vanilla. What is the probability that it came from Bowl 1?\n",
    "\n",
    "The prior probability is 50%, so the prior odds are 1. The likelihood ratio is $\\frac{3}{4} / \\frac{1}{2}$, or $3/2$. So the posterior odds are $3/2$, which corresponds to probability $3/5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.903843Z",
     "iopub.status.busy": "2021-04-16T19:35:25.903087Z",
     "iopub.status.idle": "2021-04-16T19:35:25.905922Z",
     "shell.execute_reply": "2021-04-16T19:35:25.906470Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prior_odds = 1\n",
    "likelihood_ratio = (3/4) / (1/2)\n",
    "post_odds = prior_odds * likelihood_ratio\n",
    "post_odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.911059Z",
     "iopub.status.busy": "2021-04-16T19:35:25.910422Z",
     "iopub.status.idle": "2021-04-16T19:35:25.913602Z",
     "shell.execute_reply": "2021-04-16T19:35:25.913967Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_prob = prob(post_odds)\n",
    "post_prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we draw another cookie and it's chocolate, we can do another update:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.918775Z",
     "iopub.status.busy": "2021-04-16T19:35:25.918156Z",
     "iopub.status.idle": "2021-04-16T19:35:25.922078Z",
     "shell.execute_reply": "2021-04-16T19:35:25.921279Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood_ratio = (1/4) / (1/2)\n",
    "post_odds *= likelihood_ratio\n",
    "post_odds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And convert back to probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.926620Z",
     "iopub.status.busy": "2021-04-16T19:35:25.926000Z",
     "iopub.status.idle": "2021-04-16T19:35:25.929931Z",
     "shell.execute_reply": "2021-04-16T19:35:25.930427Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.42857142857142855"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_prob = prob(post_odds)\n",
    "post_prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Oliver's Blood\n",
    "\n",
    "I’ll use Bayes’s Rule to solve another problem from MacKay’s\n",
    "[*Information Theory, Inference, and Learning Algorithms*](https://www.inference.org.uk/mackay/itila/):\n",
    "\n",
    "> Two people have left traces of their own blood at the scene of a crime. A suspect, Oliver, is tested and found to have type ‘O’ blood. The blood groups of the two traces are found to be of type ‘O’ (a common type in the local population, having frequency 60%) and of type ‘AB’ (a rare type, with frequency 1%). Do these data \\[the traces found at the scene\\] give evidence in favor of the proposition that Oliver was one of the people \\[who left blood at the scene\\]?\n",
    "\n",
    "To answer this question, we need to think about what it means for data\n",
    "to give evidence in favor of (or against) a hypothesis. Intuitively, we might say that data favor a hypothesis if the hypothesis is more likely in light of the data than it was before.\n",
    "\n",
    "In the cookie problem, the prior odds are 1, which corresponds to probability 50%. The posterior odds are $3/2$, or probability 60%. So the vanilla cookie is evidence in favor of Bowl 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bayes's Rule provides a way to make this intuition more precise. Again\n",
    "\n",
    "$$\\mathrm{odds}(A|D) = \\mathrm{odds}(A)~\\frac{P(D|A)}{P(D|B)}$$\n",
    "\n",
    "Dividing through by $\\mathrm{odds}(A)$, we get: \n",
    "\n",
    "$$\\frac{\\mathrm{odds}(A|D)}{\\mathrm{odds}(A)} = \\frac{P(D|A)}{P(D|B)}$$\n",
    "\n",
    "The term on the left is the ratio of the posterior and prior odds. The term on the right is the likelihood ratio, also called the **Bayes\n",
    "factor**.\n",
    "\n",
    "If the Bayes factor is greater than 1, that means that the data were\n",
    "more likely under $A$ than under $B$. And that means that the odds are\n",
    "greater, in light of the data, than they were before.\n",
    "\n",
    "If the Bayes factor is less than 1, that means the data were less likely under $A$ than under $B$, so the odds in favor of $A$ go down.\n",
    "\n",
    "Finally, if the Bayes factor is exactly 1, the data are equally likely\n",
    "under either hypothesis, so the odds do not change."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's apply that to the problem at hand. If Oliver is one of the people who left blood at the crime scene, he accounts for the ‘O’ sample; in that case, the probability of the data is the probability that a random member of the population has type ‘AB’ blood, which is 1%.\n",
    "\n",
    "If Oliver did not leave blood at the scene, we have two samples to\n",
    "account for. \n",
    "If we choose two random people from the population, what is the chance of finding one with type ‘O’ and one with type ‘AB’? \n",
    "Well, there are two ways it might happen: \n",
    "\n",
    "* The first person might have ‘O’ and the second ‘AB’, \n",
    "\n",
    "* Or the first person might have ‘AB’ and the second ‘O’.\n",
    "\n",
    "The probability of either combination is $(0.6) (0.01)$, which is 0.6%, so the total probability is twice that, or 1.2%.\n",
    "So the data are a little more likely if Oliver is *not* one of the people who left blood at the scene.\n",
    "\n",
    "We can use these probabilities to compute the likelihood ratio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.935512Z",
     "iopub.status.busy": "2021-04-16T19:35:25.934799Z",
     "iopub.status.idle": "2021-04-16T19:35:25.940814Z",
     "shell.execute_reply": "2021-04-16T19:35:25.940217Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8333333333333334"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "like1 = 0.01\n",
    "like2 = 2 * 0.6 * 0.01\n",
    "\n",
    "likelihood_ratio = like1 / like2\n",
    "likelihood_ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the likelihood ratio is less than 1, the blood tests are evidence *against* the hypothesis that Oliver left blood at the scence.\n",
    "\n",
    "But it is weak evidence.  For example, if the prior odds were 1 (that is, 50% probability), the posterior odds would be 0.83, which corresponds to a probability of 45%:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.943890Z",
     "iopub.status.busy": "2021-04-16T19:35:25.943238Z",
     "iopub.status.idle": "2021-04-16T19:35:25.948722Z",
     "shell.execute_reply": "2021-04-16T19:35:25.949237Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45454545454545453"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_odds = 1 * like1 / like2\n",
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this evidence doesn't \"move the needle\" very much.\n",
    "\n",
    "This example is a little contrived, but it demonstrates the\n",
    "counterintuitive result that data *consistent* with a hypothesis are\n",
    "not necessarily *in favor of* the hypothesis.\n",
    "\n",
    "If this result still bothers you, this way of thinking might help: the\n",
    "data consist of a common event, type ‘O’ blood, and a rare event, type\n",
    "‘AB’ blood. If Oliver accounts for the common event, that leaves the\n",
    "rare event unexplained. If Oliver doesn’t account for the ‘O’ blood, we\n",
    "have two chances to find someone in the population with ‘AB’ blood. And\n",
    "that factor of two makes the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Suppose that based on other evidence, you prior belief in Oliver's guilt is 90%.  How much would the blood evidence in this section change your beliefs?  What if you initially thought there was only a 10% chance of his guilt?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.953967Z",
     "iopub.status.busy": "2021-04-16T19:35:25.953380Z",
     "iopub.status.idle": "2021-04-16T19:35:25.956711Z",
     "shell.execute_reply": "2021-04-16T19:35:25.957322Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8823529411764706"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "post_odds = odds(0.9) * like1 / like2\n",
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.961924Z",
     "iopub.status.busy": "2021-04-16T19:35:25.961197Z",
     "iopub.status.idle": "2021-04-16T19:35:25.965746Z",
     "shell.execute_reply": "2021-04-16T19:35:25.965223Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0847457627118644"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "post_odds = odds(0.1) * like1 / like2\n",
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Addends\n",
    "\n",
    "The second half of this chapter is about distributions of sums and results of other operations.\n",
    "We'll start with a forward problem, where we are given the inputs and compute the distribution of the output.\n",
    "Then we'll work on inverse problems, where we are given the outputs and we compute the distribution of the inputs.\n",
    "\n",
    "As a first example, suppose you roll two dice and add them up. What is the distribution of the sum? \n",
    "I’ll use the following function to create a `Pmf` that represents the\n",
    "possible outcomes of a die:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.970626Z",
     "iopub.status.busy": "2021-04-16T19:35:25.969863Z",
     "iopub.status.idle": "2021-04-16T19:35:25.972711Z",
     "shell.execute_reply": "2021-04-16T19:35:25.971836Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from empiricaldist import Pmf\n",
    "\n",
    "def make_die(sides):\n",
    "    outcomes = np.arange(1, sides+1)\n",
    "    die = Pmf(1/sides, outcomes)\n",
    "    return die"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On a six-sided die, the outcomes are 1 through 6, all\n",
    "equally likely."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.977624Z",
     "iopub.status.busy": "2021-04-16T19:35:25.976820Z",
     "iopub.status.idle": "2021-04-16T19:35:25.980388Z",
     "shell.execute_reply": "2021-04-16T19:35:25.980927Z"
    }
   },
   "outputs": [],
   "source": [
    "die = make_die(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:25.985499Z",
     "iopub.status.busy": "2021-04-16T19:35:25.984796Z",
     "iopub.status.idle": "2021-04-16T19:35:26.189007Z",
     "shell.execute_reply": "2021-04-16T19:35:26.188413Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from utils import decorate\n",
    "\n",
    "die.bar(alpha=0.4)\n",
    "decorate(xlabel='Outcome',\n",
    "         ylabel='PMF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we roll two dice and add them up, there are 11 possible outcomes, 2\n",
    "through 12, but they are not equally likely. To compute the distribution\n",
    "of the sum, we have to enumerate the possible outcomes. \n",
    "\n",
    "And that's how this function works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.193192Z",
     "iopub.status.busy": "2021-04-16T19:35:26.192722Z",
     "iopub.status.idle": "2021-04-16T19:35:26.194939Z",
     "shell.execute_reply": "2021-04-16T19:35:26.194501Z"
    }
   },
   "outputs": [],
   "source": [
    "def add_dist(pmf1, pmf2):\n",
    "    \"\"\"Compute the distribution of a sum.\"\"\"\n",
    "    res = Pmf()\n",
    "    for q1, p1 in pmf1.items():\n",
    "        for q2, p2 in pmf2.items():\n",
    "            q = q1 + q2\n",
    "            p = p1 * p2\n",
    "            res[q] = res(q) + p\n",
    "    return res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameters are `Pmf` objects representing distributions.\n",
    "\n",
    "The loops iterate though the quantities and probabilities in the `Pmf` objects.\n",
    "Each time through the loop `q` gets the sum of a pair of quantities, and `p` gets the probability of the pair.\n",
    "Because the same sum might appear more than once, we have to add up the total probability for each sum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice a subtle element of this line:\n",
    "\n",
    "```\n",
    "            res[q] = res(q) + p\n",
    "```\n",
    "\n",
    "I use parentheses on the right side of the assignment, which returns 0 if `q` does not appear yet in `res`.\n",
    "I use brackets on the left side of the assignment to create or update an element in `res`; using parentheses on the left side would not work.\n",
    "\n",
    "`Pmf` provides `add_dist`, which does the same thing.\n",
    "You can call it as a method, like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.199932Z",
     "iopub.status.busy": "2021-04-16T19:35:26.199258Z",
     "iopub.status.idle": "2021-04-16T19:35:26.200896Z",
     "shell.execute_reply": "2021-04-16T19:35:26.201275Z"
    }
   },
   "outputs": [],
   "source": [
    "twice = die.add_dist(die)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or as a function, like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.205592Z",
     "iopub.status.busy": "2021-04-16T19:35:26.205163Z",
     "iopub.status.idle": "2021-04-16T19:35:26.206990Z",
     "shell.execute_reply": "2021-04-16T19:35:26.206626Z"
    }
   },
   "outputs": [],
   "source": [
    "twice = Pmf.add_dist(die, die)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what the result looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.210188Z",
     "iopub.status.busy": "2021-04-16T19:35:26.209766Z",
     "iopub.status.idle": "2021-04-16T19:35:26.211302Z",
     "shell.execute_reply": "2021-04-16T19:35:26.211647Z"
    },
    "tags": [
     "hide-cell"
    ]
   },
   "outputs": [],
   "source": [
    "from utils import decorate\n",
    "\n",
    "def decorate_dice(title=''):\n",
    "    decorate(xlabel='Outcome',\n",
    "             ylabel='PMF',\n",
    "             title=title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.239441Z",
     "iopub.status.busy": "2021-04-16T19:35:26.238769Z",
     "iopub.status.idle": "2021-04-16T19:35:26.367977Z",
     "shell.execute_reply": "2021-04-16T19:35:26.368514Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "twice = add_dist(die, die)\n",
    "twice.bar(color='C1', alpha=0.5)\n",
    "decorate_dice()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have a sequence of `Pmf` objects that represent dice, we can compute the distribution of the sum like this:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.371912Z",
     "iopub.status.busy": "2021-04-16T19:35:26.371501Z",
     "iopub.status.idle": "2021-04-16T19:35:26.374367Z",
     "shell.execute_reply": "2021-04-16T19:35:26.374905Z"
    }
   },
   "outputs": [],
   "source": [
    "def add_dist_seq(seq):\n",
    "    \"\"\"Compute Pmf of the sum of values from seq.\"\"\"\n",
    "    total = seq[0]\n",
    "    for other in seq[1:]:\n",
    "        total = total.add_dist(other)\n",
    "    return total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an example, we can make a list of three dice like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.378258Z",
     "iopub.status.busy": "2021-04-16T19:35:26.377654Z",
     "iopub.status.idle": "2021-04-16T19:35:26.380487Z",
     "shell.execute_reply": "2021-04-16T19:35:26.380982Z"
    }
   },
   "outputs": [],
   "source": [
    "dice = [die] * 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can compute the distribution of their sum like this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.385882Z",
     "iopub.status.busy": "2021-04-16T19:35:26.385458Z",
     "iopub.status.idle": "2021-04-16T19:35:26.388695Z",
     "shell.execute_reply": "2021-04-16T19:35:26.389169Z"
    }
   },
   "outputs": [],
   "source": [
    "thrice = add_dist_seq(dice)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following figure shows what these three distributions look like:\n",
    "\n",
    "-   The distribution of a single die is uniform from 1 to 6.\n",
    "\n",
    "-   The sum of two dice has a triangle distribution between 2 and 12.\n",
    "\n",
    "-   The sum of three dice has a bell-shaped distribution between 3\n",
    "    and 18."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.421840Z",
     "iopub.status.busy": "2021-04-16T19:35:26.406759Z",
     "iopub.status.idle": "2021-04-16T19:35:26.603342Z",
     "shell.execute_reply": "2021-04-16T19:35:26.602970Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "die.plot(label='once')\n",
    "twice.plot(label='twice', ls='--')\n",
    "thrice.plot(label='thrice', ls=':')\n",
    "\n",
    "plt.xticks([0,3,6,9,12,15,18])\n",
    "decorate_dice(title='Distributions of sums')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an aside, this example demonstrates the Central Limit Theorem, which says that the distribution of a sum converges on a bell-shaped normal distribution, at least under some conditions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gluten Sensitivity\n",
    "\n",
    "In 2015 I read a paper that tested whether people diagnosed with gluten sensitivity (but not celiac disease) were able to distinguish gluten flour from non-gluten flour in a blind challenge\n",
    "([you can read the paper here](https://onlinelibrary.wiley.com/doi/full/10.1111/apt.13372)).\n",
    "\n",
    "Out of 35 subjects, 12 correctly identified the gluten flour based on\n",
    "resumption of symptoms while they were eating it. Another 17 wrongly\n",
    "identified the gluten-free flour based on their symptoms, and 6 were\n",
    "unable to distinguish.\n",
    "\n",
    "The authors conclude, \"Double-blind gluten challenge induces symptom\n",
    "recurrence in just one-third of patients.\"\n",
    "\n",
    "This conclusion seems odd to me, because if none of the patients were\n",
    "sensitive to gluten, we would expect some of them to identify the gluten flour by chance. \n",
    "So here's the question: based on this data, how many of the subjects are sensitive to gluten and how many are guessing?\n",
    "\n",
    "We can use Bayes's Theorem to answer this question, but first we have to make some modeling decisions. I'll assume:\n",
    "\n",
    "-   People who are sensitive to gluten have a 95% chance of correctly\n",
    "    identifying gluten flour under the challenge conditions, and\n",
    "\n",
    "-   People who are not sensitive have a 40% chance of identifying the\n",
    "    gluten flour by chance (and a 60% chance of either choosing the\n",
    "    other flour or failing to distinguish).\n",
    "\n",
    "These particular values are arbitrary, but the results are not sensitive to these choices.\n",
    "\n",
    "I will solve this problem in two steps. First, assuming that we know how many subjects are sensitive, I will compute the distribution of the data. \n",
    "Then, using the likelihood of the data, I will compute the posterior distribution of the number of sensitive patients.\n",
    "\n",
    "The first is the **forward problem**; the second is the **inverse\n",
    "problem**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Forward Problem\n",
    "\n",
    "Suppose we know that 10 of the 35 subjects are sensitive to gluten. That\n",
    "means that 25 are not:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.606680Z",
     "iopub.status.busy": "2021-04-16T19:35:26.606215Z",
     "iopub.status.idle": "2021-04-16T19:35:26.607888Z",
     "shell.execute_reply": "2021-04-16T19:35:26.608296Z"
    }
   },
   "outputs": [],
   "source": [
    "n = 35\n",
    "num_sensitive = 10\n",
    "num_insensitive = n - num_sensitive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each sensitive subject has a 95% chance of identifying the gluten flour,\n",
    "so the number of correct identifications follows a binomial distribution.\n",
    "\n",
    "I'll use `make_binomial`, which we defined in <<_TheBinomialDistribution>>, to make a `Pmf` that represents the binomial distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.612684Z",
     "iopub.status.busy": "2021-04-16T19:35:26.612204Z",
     "iopub.status.idle": "2021-04-16T19:35:26.613941Z",
     "shell.execute_reply": "2021-04-16T19:35:26.614305Z"
    }
   },
   "outputs": [],
   "source": [
    "from utils import make_binomial\n",
    "\n",
    "dist_sensitive = make_binomial(num_sensitive, 0.95)\n",
    "dist_insensitive = make_binomial(num_insensitive, 0.40)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are the distributions for the number of correct identifications in each group.\n",
    "\n",
    "Now we can use `add_dist` to compute the distribution of the total number of correct identifications:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.618422Z",
     "iopub.status.busy": "2021-04-16T19:35:26.618001Z",
     "iopub.status.idle": "2021-04-16T19:35:26.620089Z",
     "shell.execute_reply": "2021-04-16T19:35:26.619662Z"
    }
   },
   "outputs": [],
   "source": [
    "dist_total = Pmf.add_dist(dist_sensitive, dist_insensitive)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.644030Z",
     "iopub.status.busy": "2021-04-16T19:35:26.631462Z",
     "iopub.status.idle": "2021-04-16T19:35:26.800922Z",
     "shell.execute_reply": "2021-04-16T19:35:26.800528Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dist_sensitive.plot(label='sensitive', ls=':')\n",
    "dist_insensitive.plot(label='insensitive', ls='--')\n",
    "dist_total.plot(label='total')\n",
    "\n",
    "decorate(xlabel='Number of correct identifications',\n",
    "         ylabel='PMF',\n",
    "         title='Gluten sensitivity')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We expect most of the sensitive subjects to identify the gluten flour correctly.\n",
    "Of the 25 insensitive subjects, we expect about 10 to identify the gluten flour by chance.\n",
    "So we expect about 20 correct identifications in total.\n",
    "\n",
    "This is the answer to the forward problem: given the number of sensitive subjects, we can compute the distribution of the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Inverse Problem\n",
    "\n",
    "Now let's solve the inverse problem: given the data, we'll compute the posterior distribution of the number of sensitive subjects.\n",
    "\n",
    "Here's how.  I'll loop through the possible values of `num_sensitive` and compute the distribution of the data for each:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.820717Z",
     "iopub.status.busy": "2021-04-16T19:35:26.819593Z",
     "iopub.status.idle": "2021-04-16T19:35:26.868275Z",
     "shell.execute_reply": "2021-04-16T19:35:26.867749Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "table = pd.DataFrame()\n",
    "for num_sensitive in range(0, n+1):\n",
    "    num_insensitive = n - num_sensitive\n",
    "    dist_sensitive = make_binomial(num_sensitive, 0.95)\n",
    "    dist_insensitive = make_binomial(num_insensitive, 0.4)\n",
    "    dist_total = Pmf.add_dist(dist_sensitive, dist_insensitive)    \n",
    "    table[num_sensitive] = dist_total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The loop enumerates the possible values of `num_sensitive`.\n",
    "For each value, it computes the distribution of the total number of correct identifications, and stores the result as a column in a Pandas `DataFrame`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.872557Z",
     "iopub.status.busy": "2021-04-16T19:35:26.871819Z",
     "iopub.status.idle": "2021-04-16T19:35:26.898135Z",
     "shell.execute_reply": "2021-04-16T19:35:26.897756Z"
    },
    "tags": [
     "hide-cell"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>26</th>\n",
       "      <th>27</th>\n",
       "      <th>28</th>\n",
       "      <th>29</th>\n",
       "      <th>30</th>\n",
       "      <th>31</th>\n",
       "      <th>32</th>\n",
       "      <th>33</th>\n",
       "      <th>34</th>\n",
       "      <th>35</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.719071e-08</td>\n",
       "      <td>1.432559e-09</td>\n",
       "      <td>1.193799e-10</td>\n",
       "      <td>9.948326e-12</td>\n",
       "      <td>8.290272e-13</td>\n",
       "      <td>6.908560e-14</td>\n",
       "      <td>5.757133e-15</td>\n",
       "      <td>4.797611e-16</td>\n",
       "      <td>3.998009e-17</td>\n",
       "      <td>3.331674e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>1.501694e-36</td>\n",
       "      <td>1.251411e-37</td>\n",
       "      <td>1.042843e-38</td>\n",
       "      <td>8.690357e-40</td>\n",
       "      <td>7.241964e-41</td>\n",
       "      <td>6.034970e-42</td>\n",
       "      <td>5.029142e-43</td>\n",
       "      <td>4.190952e-44</td>\n",
       "      <td>3.492460e-45</td>\n",
       "      <td>2.910383e-46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.011165e-07</td>\n",
       "      <td>5.968996e-08</td>\n",
       "      <td>7.162795e-09</td>\n",
       "      <td>7.792856e-10</td>\n",
       "      <td>8.013930e-11</td>\n",
       "      <td>7.944844e-12</td>\n",
       "      <td>7.676178e-13</td>\n",
       "      <td>7.276377e-14</td>\n",
       "      <td>6.796616e-15</td>\n",
       "      <td>6.274653e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>7.508469e-34</td>\n",
       "      <td>6.486483e-35</td>\n",
       "      <td>5.596590e-36</td>\n",
       "      <td>4.823148e-37</td>\n",
       "      <td>4.152060e-38</td>\n",
       "      <td>3.570691e-39</td>\n",
       "      <td>3.067777e-40</td>\n",
       "      <td>2.633315e-41</td>\n",
       "      <td>2.258457e-42</td>\n",
       "      <td>1.935405e-43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.545987e-06</td>\n",
       "      <td>9.741401e-07</td>\n",
       "      <td>1.709122e-07</td>\n",
       "      <td>2.506426e-08</td>\n",
       "      <td>3.269131e-09</td>\n",
       "      <td>3.940182e-10</td>\n",
       "      <td>4.490244e-11</td>\n",
       "      <td>4.908756e-12</td>\n",
       "      <td>5.197412e-13</td>\n",
       "      <td>5.365476e-14</td>\n",
       "      <td>...</td>\n",
       "      <td>1.806613e-31</td>\n",
       "      <td>1.620070e-32</td>\n",
       "      <td>1.449030e-33</td>\n",
       "      <td>1.292922e-34</td>\n",
       "      <td>1.151034e-35</td>\n",
       "      <td>1.022555e-36</td>\n",
       "      <td>9.066202e-38</td>\n",
       "      <td>8.023344e-39</td>\n",
       "      <td>7.088005e-40</td>\n",
       "      <td>6.251357e-41</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3 rows × 36 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             0             1             2             3             4   \\\n",
       "0  1.719071e-08  1.432559e-09  1.193799e-10  9.948326e-12  8.290272e-13   \n",
       "1  4.011165e-07  5.968996e-08  7.162795e-09  7.792856e-10  8.013930e-11   \n",
       "2  4.545987e-06  9.741401e-07  1.709122e-07  2.506426e-08  3.269131e-09   \n",
       "\n",
       "             5             6             7             8             9   ...  \\\n",
       "0  6.908560e-14  5.757133e-15  4.797611e-16  3.998009e-17  3.331674e-18  ...   \n",
       "1  7.944844e-12  7.676178e-13  7.276377e-14  6.796616e-15  6.274653e-16  ...   \n",
       "2  3.940182e-10  4.490244e-11  4.908756e-12  5.197412e-13  5.365476e-14  ...   \n",
       "\n",
       "             26            27            28            29            30  \\\n",
       "0  1.501694e-36  1.251411e-37  1.042843e-38  8.690357e-40  7.241964e-41   \n",
       "1  7.508469e-34  6.486483e-35  5.596590e-36  4.823148e-37  4.152060e-38   \n",
       "2  1.806613e-31  1.620070e-32  1.449030e-33  1.292922e-34  1.151034e-35   \n",
       "\n",
       "             31            32            33            34            35  \n",
       "0  6.034970e-42  5.029142e-43  4.190952e-44  3.492460e-45  2.910383e-46  \n",
       "1  3.570691e-39  3.067777e-40  2.633315e-41  2.258457e-42  1.935405e-43  \n",
       "2  1.022555e-36  9.066202e-38  8.023344e-39  7.088005e-40  6.251357e-41  \n",
       "\n",
       "[3 rows x 36 columns]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following figure shows selected columns from the `DataFrame`, corresponding to different hypothetical values of `num_sensitive`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:26.936312Z",
     "iopub.status.busy": "2021-04-16T19:35:26.919136Z",
     "iopub.status.idle": "2021-04-16T19:35:27.103426Z",
     "shell.execute_reply": "2021-04-16T19:35:27.102967Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table[0].plot(label='num_sensitive = 0')\n",
    "table[10].plot(label='num_sensitive = 10')\n",
    "table[20].plot(label='num_sensitive = 20', ls='--')\n",
    "table[30].plot(label='num_sensitive = 30', ls=':')\n",
    "    \n",
    "decorate(xlabel='Number of correct identifications',\n",
    "         ylabel='PMF',\n",
    "         title='Gluten sensitivity')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use this table to compute the likelihood of the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.107058Z",
     "iopub.status.busy": "2021-04-16T19:35:27.106504Z",
     "iopub.status.idle": "2021-04-16T19:35:27.109131Z",
     "shell.execute_reply": "2021-04-16T19:35:27.109567Z"
    }
   },
   "outputs": [],
   "source": [
    "likelihood1 = table.loc[12]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`loc` selects a row from the `DataFrame`.\n",
    "The row with index 12 contains the probability of 12 correct identifications for each hypothetical value of `num_sensitive`.\n",
    "And that's exactly the likelihood we need to do a Bayesian update.\n",
    "\n",
    "I'll use a uniform prior, which implies that I would be equally surprised by any value of `num_sensitive`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.113201Z",
     "iopub.status.busy": "2021-04-16T19:35:27.112749Z",
     "iopub.status.idle": "2021-04-16T19:35:27.115326Z",
     "shell.execute_reply": "2021-04-16T19:35:27.114769Z"
    }
   },
   "outputs": [],
   "source": [
    "hypos = np.arange(n+1)\n",
    "prior = Pmf(1, hypos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the update:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.119898Z",
     "iopub.status.busy": "2021-04-16T19:35:27.119367Z",
     "iopub.status.idle": "2021-04-16T19:35:27.127041Z",
     "shell.execute_reply": "2021-04-16T19:35:27.126620Z"
    },
    "tags": [
     "hide-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4754741648615131"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior1 = prior * likelihood1\n",
    "posterior1.normalize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For comparison, I also compute the posterior for another possible outcome, 20 correct identifications."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.132181Z",
     "iopub.status.busy": "2021-04-16T19:35:27.131596Z",
     "iopub.status.idle": "2021-04-16T19:35:27.133996Z",
     "shell.execute_reply": "2021-04-16T19:35:27.134357Z"
    },
    "tags": [
     "hide-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7818649765887378"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood2 = table.loc[20]\n",
    "posterior2 = prior * likelihood2\n",
    "posterior2.normalize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following figure shows posterior distributions of `num_sensitive` based on the actual data, 12 correct identifications, and the other possible outcome, 20 correct identifications."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.180198Z",
     "iopub.status.busy": "2021-04-16T19:35:27.174890Z",
     "iopub.status.idle": "2021-04-16T19:35:27.299021Z",
     "shell.execute_reply": "2021-04-16T19:35:27.298634Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior1.plot(label='posterior with 12 correct', color='C4')\n",
    "posterior2.plot(label='posterior with 20 correct', color='C1')\n",
    "\n",
    "decorate(xlabel='Number of sensitive subjects',\n",
    "         ylabel='PMF',\n",
    "         title='Posterior distributions')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With 12 correct identifications, the most likely conclusion is that none of the subjects are sensitive to gluten.\n",
    "If there had been 20 correct identifications, the most likely conclusion would be that 11-12 of the subjects were sensitive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.302382Z",
     "iopub.status.busy": "2021-04-16T19:35:27.301973Z",
     "iopub.status.idle": "2021-04-16T19:35:27.306032Z",
     "shell.execute_reply": "2021-04-16T19:35:27.306511Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior1.max_prob()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.310142Z",
     "iopub.status.busy": "2021-04-16T19:35:27.309624Z",
     "iopub.status.idle": "2021-04-16T19:35:27.311979Z",
     "shell.execute_reply": "2021-04-16T19:35:27.312474Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior2.max_prob()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "This chapter presents two topics that are almost unrelated except that they make the title of the chapter catchy.\n",
    "\n",
    "The first part of the chapter is about Bayes's Rule, evidence, and how we can quantify the strength of evidence using a likelihood ratio or Bayes factor.\n",
    "\n",
    "The second part is about `add_dist`, which computes the distribution of a sum.\n",
    "We can use this function to solve forward and inverse problems; that is, given the parameters of a system, we can compute the distribution of the data or, given the data, we can compute the distribution of the parameters.\n",
    "\n",
    "In the next chapter, we'll compute distributions for minimums and maximums, and use them to solve more Bayesian problems.\n",
    "But first you might want to work on these exercises."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Let's use Bayes's Rule to solve the Elvis problem from <<_Distributions>>:\n",
    "\n",
    "> Elvis Presley had a twin brother who died at birth. What is the probability that Elvis was an identical twin?\n",
    "\n",
    "In 1935, about 2/3 of twins were fraternal and 1/3 were identical.\n",
    "The question contains two pieces of information we can use to update this prior.\n",
    "\n",
    "* First, Elvis's twin was also male, which is more likely if they were identical twins, with a likelihood ratio of 2.\n",
    "\n",
    "* Also, Elvis's twin died at birth, which is more likely if they were identical twins, with a likelihood ratio of 1.25.\n",
    "\n",
    "If you are curious about where those numbers come from, I wrote [a blog post about it](https://www.allendowney.com/blog/2020/01/28/the-elvis-problem-revisited)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.315665Z",
     "iopub.status.busy": "2021-04-16T19:35:27.315244Z",
     "iopub.status.idle": "2021-04-16T19:35:27.317350Z",
     "shell.execute_reply": "2021-04-16T19:35:27.317875Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "prior_odds = odds(1/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.320891Z",
     "iopub.status.busy": "2021-04-16T19:35:27.320486Z",
     "iopub.status.idle": "2021-04-16T19:35:27.322254Z",
     "shell.execute_reply": "2021-04-16T19:35:27.322625Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "post_odds = prior_odds * 2 * 1.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.326406Z",
     "iopub.status.busy": "2021-04-16T19:35:27.325724Z",
     "iopub.status.idle": "2021-04-16T19:35:27.328858Z",
     "shell.execute_reply": "2021-04-16T19:35:27.328390Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5555555555555555"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** The following is an [interview question that appeared on glassdoor.com](https://www.glassdoor.com/Interview/You-re-about-to-get-on-a-plane-to-Seattle-You-want-to-know-if-you-should-bring-an-umbrella-You-call-3-random-friends-of-y-QTN_519262.htm), attributed to Facebook:\n",
    "\n",
    "> You're about to get on a plane to Seattle. You want to know if you should bring an umbrella. You call 3 random friends of yours who live there and ask each independently if it's raining. Each of your friends has a 2/3 chance of telling you the truth and a 1/3 chance of messing with you by lying. All 3 friends tell you that \"Yes\" it is raining. What is the probability that it's actually raining in Seattle?\n",
    "\n",
    "Use Bayes's Rule to solve this problem.  As a prior you can assume that it rains in Seattle about 10% of the time.\n",
    "\n",
    "This question causes some confusion about the differences between Bayesian and frequentist interpretations of probability; if you are curious about this point, [I wrote a blog article about it](http://allendowney.blogspot.com/2016/09/bayess-theorem-is-not-optional.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.332446Z",
     "iopub.status.busy": "2021-04-16T19:35:27.331910Z",
     "iopub.status.idle": "2021-04-16T19:35:27.333826Z",
     "shell.execute_reply": "2021-04-16T19:35:27.334261Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "prior_odds = odds(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.337763Z",
     "iopub.status.busy": "2021-04-16T19:35:27.337222Z",
     "iopub.status.idle": "2021-04-16T19:35:27.339316Z",
     "shell.execute_reply": "2021-04-16T19:35:27.339799Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "post_odds = prior_odds * 2 * 2 * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.344018Z",
     "iopub.status.busy": "2021-04-16T19:35:27.343298Z",
     "iopub.status.idle": "2021-04-16T19:35:27.346940Z",
     "shell.execute_reply": "2021-04-16T19:35:27.346413Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4705882352941177"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** [According to the CDC](https://www.cdc.gov/tobacco/data_statistics/fact_sheets/health_effects/effects_cig_smoking), people who smoke are about 25 times more likely to develop lung cancer than nonsmokers.\n",
    "\n",
    "[Also according to the CDC](https://www.cdc.gov/tobacco/data_statistics/fact_sheets/adult_data/cig_smoking/index.htm), about 14\\% of adults in the U.S. are smokers.\n",
    "If you learn that someone has lung cancer, what is the probability they are a smoker?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.350794Z",
     "iopub.status.busy": "2021-04-16T19:35:27.350217Z",
     "iopub.status.idle": "2021-04-16T19:35:27.352716Z",
     "shell.execute_reply": "2021-04-16T19:35:27.352226Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "prior_odds = odds(0.14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.356825Z",
     "iopub.status.busy": "2021-04-16T19:35:27.356098Z",
     "iopub.status.idle": "2021-04-16T19:35:27.358326Z",
     "shell.execute_reply": "2021-04-16T19:35:27.358809Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "post_odds = prior_odds * 25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.363702Z",
     "iopub.status.busy": "2021-04-16T19:35:27.362765Z",
     "iopub.status.idle": "2021-04-16T19:35:27.365904Z",
     "shell.execute_reply": "2021-04-16T19:35:27.366304Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8027522935779816"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "prob(post_odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** In *Dungeons & Dragons*, the amount of damage a goblin can withstand is the sum of two six-sided dice. The amount of damage you inflict with a short sword is determined by rolling one six-sided die.\n",
    "A goblin is defeated if the total damage you inflict is greater than or equal to the amount it can withstand.\n",
    "\n",
    "Suppose you are fighting a goblin and you have already inflicted 3 points of damage. What is your probability of defeating the goblin with your next successful attack?\n",
    "\n",
    "Hint: You can use `Pmf.sub_dist` to subtract a constant amount, like 3, from a `Pmf`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.370205Z",
     "iopub.status.busy": "2021-04-16T19:35:27.369557Z",
     "iopub.status.idle": "2021-04-16T19:35:27.371649Z",
     "shell.execute_reply": "2021-04-16T19:35:27.371182Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "d6 = make_die(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.375761Z",
     "iopub.status.busy": "2021-04-16T19:35:27.375251Z",
     "iopub.status.idle": "2021-04-16T19:35:27.377911Z",
     "shell.execute_reply": "2021-04-16T19:35:27.377227Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "# The amount the goblin started with is the sum of two d6\n",
    "hp_before = Pmf.add_dist(d6, d6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-1</th>\n",
       "      <td>0.027778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.055556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.138889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.138889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.055556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.027778</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "-1    0.027778\n",
       " 0    0.055556\n",
       " 1    0.083333\n",
       " 2    0.111111\n",
       " 3    0.138889\n",
       " 4    0.166667\n",
       " 5    0.138889\n",
       " 6    0.111111\n",
       " 7    0.083333\n",
       " 8    0.055556\n",
       " 9    0.027778\n",
       "dtype: float64"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "# Here's the number of hit points after the first attack\n",
    "hp_after = Pmf.sub_dist(hp_before, 3)\n",
    "hp_after"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-1</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.090909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.121212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.151515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.181818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.151515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.121212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.090909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.060606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.030303</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "-1    0.000000\n",
       " 0    0.000000\n",
       " 1    0.090909\n",
       " 2    0.121212\n",
       " 3    0.151515\n",
       " 4    0.181818\n",
       " 5    0.151515\n",
       " 6    0.121212\n",
       " 7    0.090909\n",
       " 8    0.060606\n",
       " 9    0.030303\n",
       "dtype: float64"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "# But -1 and 0 are not possible, because in that case the goblin would be defeated.\n",
    "# So we have to zero them out and renormalize\n",
    "hp_after[[-1, 0]] = 0\n",
    "hp_after.normalize()\n",
    "hp_after"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.382061Z",
     "iopub.status.busy": "2021-04-16T19:35:27.381402Z",
     "iopub.status.idle": "2021-04-16T19:35:27.383660Z",
     "shell.execute_reply": "2021-04-16T19:35:27.383155Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "# The damage from the second attack is one d6\n",
    "damage = d6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.424920Z",
     "iopub.status.busy": "2021-04-16T19:35:27.406232Z",
     "iopub.status.idle": "2021-04-16T19:35:27.539862Z",
     "shell.execute_reply": "2021-04-16T19:35:27.539344Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "# Here's what the distributions look like\n",
    "hp_after.bar(label='Hit points')\n",
    "damage.plot(label='Damage', color='C1')\n",
    "decorate_dice('The Goblin Problem')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.544172Z",
     "iopub.status.busy": "2021-04-16T19:35:27.543760Z",
     "iopub.status.idle": "2021-04-16T19:35:27.546538Z",
     "shell.execute_reply": "2021-04-16T19:35:27.547016Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's the distribution of points the goblin has left\n",
    "points_left = Pmf.sub_dist(hp_after, damage)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.550649Z",
     "iopub.status.busy": "2021-04-16T19:35:27.550237Z",
     "iopub.status.idle": "2021-04-16T19:35:27.555283Z",
     "shell.execute_reply": "2021-04-16T19:35:27.554906Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4545454545454545"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# And here's the probability the goblin is dead\n",
    "points_left.prob_le(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Suppose I have a box with a 6-sided die, an 8-sided die, and a 12-sided die.\n",
    "I choose one of the dice at random, roll it twice, multiply the outcomes, and report that the product is 12.\n",
    "What is the probability that I chose the 8-sided die?\n",
    "\n",
    "Hint: `Pmf` provides a function called `mul_dist` that takes two `Pmf` objects and returns a `Pmf` that represents the distribution of the product."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.559242Z",
     "iopub.status.busy": "2021-04-16T19:35:27.558669Z",
     "iopub.status.idle": "2021-04-16T19:35:27.560621Z",
     "shell.execute_reply": "2021-04-16T19:35:27.561052Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "hypos = [6, 8, 12]\n",
    "prior = Pmf(1, hypos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.570896Z",
     "iopub.status.busy": "2021-04-16T19:35:27.570353Z",
     "iopub.status.idle": "2021-04-16T19:35:27.574763Z",
     "shell.execute_reply": "2021-04-16T19:35:27.575226Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.1875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.0625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.0625</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "1     0.0625\n",
       "2     0.1250\n",
       "3     0.1250\n",
       "4     0.1875\n",
       "6     0.1250\n",
       "8     0.1250\n",
       "9     0.0625\n",
       "12    0.1250\n",
       "16    0.0625\n",
       "dtype: float64"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's the distribution of the product for the 4-sided die\n",
    "\n",
    "d4 = make_die(4)\n",
    "Pmf.mul_dist(d4, d4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.582633Z",
     "iopub.status.busy": "2021-04-16T19:35:27.580097Z",
     "iopub.status.idle": "2021-04-16T19:35:27.584876Z",
     "shell.execute_reply": "2021-04-16T19:35:27.585267Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.1111111111111111, 0.0625, 0.041666666666666664]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's the likelihood of getting a 12 for each die\n",
    "likelihood = []\n",
    "\n",
    "for sides in hypos:\n",
    "    die = make_die(sides)\n",
    "    pmf = Pmf.mul_dist(die, die)\n",
    "    likelihood.append(pmf[12])\n",
    "    \n",
    "likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.591475Z",
     "iopub.status.busy": "2021-04-16T19:35:27.590954Z",
     "iopub.status.idle": "2021-04-16T19:35:27.593367Z",
     "shell.execute_reply": "2021-04-16T19:35:27.593715Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.516129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.290323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.193548</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "6     0.516129\n",
       "8     0.290323\n",
       "12    0.193548\n",
       "dtype: float64"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# And here's the update\n",
    "posterior = prior * likelihood\n",
    "posterior.normalize()\n",
    "posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** *Betrayal at House on the Hill* is a strategy game in which characters with different attributes explore a haunted house.  Depending on their attributes, the characters roll different numbers of dice.  For example, if attempting a task that depends on knowledge, Professor Longfellow rolls 5 dice, Madame Zostra rolls 4, and Ox Bellows rolls 3.  Each die yields 0, 1, or 2 with equal probability.  \n",
    "\n",
    "If a randomly chosen character attempts a task three times and rolls a total of 3 on the first attempt, 4 on the second, and 5 on the third, which character do you think it was?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.599975Z",
     "iopub.status.busy": "2021-04-16T19:35:27.599314Z",
     "iopub.status.idle": "2021-04-16T19:35:27.602133Z",
     "shell.execute_reply": "2021-04-16T19:35:27.602555Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "0    0.333333\n",
       "1    0.333333\n",
       "2    0.333333\n",
       "dtype: float64"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "die = Pmf(1/3, [0,1,2])\n",
    "die"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.614916Z",
     "iopub.status.busy": "2021-04-16T19:35:27.614014Z",
     "iopub.status.idle": "2021-04-16T19:35:27.619438Z",
     "shell.execute_reply": "2021-04-16T19:35:27.619807Z"
    }
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "pmfs = {}\n",
    "pmfs['Bellows'] = add_dist_seq([die]*3)\n",
    "pmfs['Zostra'] = add_dist_seq([die]*4)\n",
    "pmfs['Longfellow'] = add_dist_seq([die]*5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.623276Z",
     "iopub.status.busy": "2021-04-16T19:35:27.622677Z",
     "iopub.status.idle": "2021-04-16T19:35:27.624942Z",
     "shell.execute_reply": "2021-04-16T19:35:27.625311Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2345679012345679"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmfs['Zostra'](4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.629708Z",
     "iopub.status.busy": "2021-04-16T19:35:27.629052Z",
     "iopub.status.idle": "2021-04-16T19:35:27.632391Z",
     "shell.execute_reply": "2021-04-16T19:35:27.631917Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00915247412224499"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmfs['Zostra']([3,4,5]).prod()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.639970Z",
     "iopub.status.busy": "2021-04-16T19:35:27.639171Z",
     "iopub.status.idle": "2021-04-16T19:35:27.642148Z",
     "shell.execute_reply": "2021-04-16T19:35:27.642611Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Bellows</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zostra</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Longfellow</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Bellows       0.333333\n",
       "Zostra        0.333333\n",
       "Longfellow    0.333333\n",
       "dtype: float64"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "hypos = pmfs.keys()\n",
    "prior = Pmf(1/3, hypos)\n",
    "prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.652015Z",
     "iopub.status.busy": "2021-04-16T19:35:27.651434Z",
     "iopub.status.idle": "2021-04-16T19:35:27.653898Z",
     "shell.execute_reply": "2021-04-16T19:35:27.654265Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Bellows</th>\n",
       "      <td>0.006401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zostra</th>\n",
       "      <td>0.009152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Longfellow</th>\n",
       "      <td>0.004798</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Bellows       0.006401\n",
       "Zostra        0.009152\n",
       "Longfellow    0.004798\n",
       "dtype: float64"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "likelihood = prior.copy()\n",
    "\n",
    "for hypo in hypos:\n",
    "    likelihood[hypo] = pmfs[hypo]([3,4,5]).prod()\n",
    "\n",
    "likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.660241Z",
     "iopub.status.busy": "2021-04-16T19:35:27.659730Z",
     "iopub.status.idle": "2021-04-16T19:35:27.662465Z",
     "shell.execute_reply": "2021-04-16T19:35:27.662071Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Bellows</th>\n",
       "      <td>0.314534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zostra</th>\n",
       "      <td>0.449704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Longfellow</th>\n",
       "      <td>0.235762</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Bellows       0.314534\n",
       "Zostra        0.449704\n",
       "Longfellow    0.235762\n",
       "dtype: float64"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "posterior = (prior * likelihood)\n",
    "posterior.normalize()\n",
    "posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** There are 538 members of the United States Congress. Suppose we audit their investment portfolios and find that 312 of them out-perform the market.\n",
    "Let's assume that an honest member of Congress has only a 50% chance of out-performing the market, but a dishonest member who trades on inside information has a 90% chance.  How many members of Congress are honest?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:27.667020Z",
     "iopub.status.busy": "2021-04-16T19:35:27.666574Z",
     "iopub.status.idle": "2021-04-16T19:35:29.234154Z",
     "shell.execute_reply": "2021-04-16T19:35:29.233711Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(539, 539)"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "n = 538\n",
    "\n",
    "ns = range(0, n+1)\n",
    "table = pd.DataFrame(index=ns, columns=ns, dtype=float)\n",
    "\n",
    "for n_honest in ns:\n",
    "    n_dishonest = n - n_honest\n",
    "\n",
    "    dist_honest = make_binomial(n_honest, 0.5)\n",
    "    dist_dishonest = make_binomial(n_dishonest, 0.9)\n",
    "    dist_total = Pmf.add_dist(dist_honest, dist_dishonest)    \n",
    "    table[n_honest] = dist_total\n",
    "    \n",
    "table.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:29.237941Z",
     "iopub.status.busy": "2021-04-16T19:35:29.237391Z",
     "iopub.status.idle": "2021-04-16T19:35:29.243431Z",
     "shell.execute_reply": "2021-04-16T19:35:29.242940Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "539"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "data = 312\n",
    "likelihood = table.loc[312]\n",
    "len(likelihood)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:29.247538Z",
     "iopub.status.busy": "2021-04-16T19:35:29.246906Z",
     "iopub.status.idle": "2021-04-16T19:35:29.249712Z",
     "shell.execute_reply": "2021-04-16T19:35:29.249309Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "539"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "hypos = np.arange(n+1)\n",
    "prior = Pmf(1, hypos)\n",
    "len(prior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:29.253937Z",
     "iopub.status.busy": "2021-04-16T19:35:29.252471Z",
     "iopub.status.idle": "2021-04-16T19:35:29.256808Z",
     "shell.execute_reply": "2021-04-16T19:35:29.256391Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "431.4882114501996"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "posterior = prior * likelihood\n",
    "posterior.normalize()\n",
    "posterior.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:29.291044Z",
     "iopub.status.busy": "2021-04-16T19:35:29.290611Z",
     "iopub.status.idle": "2021-04-16T19:35:29.403725Z",
     "shell.execute_reply": "2021-04-16T19:35:29.403346Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "posterior.plot(label='posterior')\n",
    "decorate(xlabel='Number of honest members of Congress',\n",
    "         ylabel='PMF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:29.407201Z",
     "iopub.status.busy": "2021-04-16T19:35:29.406723Z",
     "iopub.status.idle": "2021-04-16T19:35:29.411010Z",
     "shell.execute_reply": "2021-04-16T19:35:29.411524Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "430"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "posterior.max_prob()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-04-16T19:35:29.415545Z",
     "iopub.status.busy": "2021-04-16T19:35:29.415072Z",
     "iopub.status.idle": "2021-04-16T19:35:29.420156Z",
     "shell.execute_reply": "2021-04-16T19:35:29.419744Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([388., 477.])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "posterior.credible_interval(0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}